Verification and Validation of High-Resolution Inviscid and Viscous Conical Nozzle Flows

Abstract

Capturing elaborated flow structures and phenomena is required for well-solved numerical flows. The finite difference methods allow simple discretization of mesh and model equations. However, they need simpler meshes, e.g., rectangular. The inverse Lax-Wendroff (ILW) procedure can handle complex geometries for rectangular meshes. High-resolution and high-order methods can capture elaborated flow structures and phenomena. They also have strong mathematical and physical backgrounds, such as positivity-preserving, jump conditions, and wave propagation concepts. We perceive an effort toward direct numerical simulation, for instance, regarding weighted essentially non-oscillatory (WENO) schemes. Thus, we propose to solve a challenging engineering application without turbulence models. We aim to verify and validate recent high-resolution and high-order methods. To check the solver accuracy, we solved vortex and Couette flows. Then, we solved inviscid and viscous nozzle flows for a conical profile. We employed the finite difference method, positivity-preserving Lax-Friedrichs splitting, high-resolution viscous terms discretization, fifth-order multi-resolution WENO, ILW, and third-order strong stability preserving Runge-Kutta. We showed the solver is high-order and captured elaborated flow structures and phenomena. One can see oblique shocks in both nozzle flows. In the viscous flow, we also captured a free-shock separation, recirculation, entrainment region, Mach disk, and the diamond-shaped pattern of nozzle flows.

Keywords

High-resolution / Compressible / Navier-Stokes / Free-shock separation / Nozzle flow

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Funding

Division of Mathematical Sciences(DMS-2010107); Air Force Office of Scientific Research(FA9550-20-1-0055)